Quark Mass Effects in Fermionic Decays of the Higgs Boson in O(αs2)O(\alpha_s^2) Perturbative QCD

The results of analytical evaluation of $O(\alpha_s^2)$ QCD contributions due to the nonvanishing quark masses to $\Gamma_{H\rightarrow q_f\overline{q}_f}$ are presented. The ``triangle anomaly'' type contributions are included. As a byproduct the $O(\alpha_s^3)$ logarithmic contributions are evaluated. The results are presented both in terms of running and pole quark masses. The partial decay modes $H \rightarrow b\overline{b}$ and $H \rightarrow c\overline{c}$ are considered. The calculated corrections decrease the absolute value of large and negative $O(\alpha_s^2)$ massless limit coefficient by $\leq 1\%$ in the intermediate mass region and by 1\%$-$20\% in the low mass region which, however, is experimentally ruled out. The results are relevant for $H \rightarrow t\overline{t}$ decay mode for the higher Higgs mass region where the mass effects are large and important. The high order corrections remove a very large discrepancy between the results for $\Gamma_{H\rightarrow q_f\overline{q}_f}$ in terms of running and pole quark masses almost completely and reduce the scale dependence from about 40\% to nearly 5\%.Comment: 16 pages, LATeX, +5 figures available upon request, preprint OITS-543 (University of Oregon, USA, May 1994). ( Additions are made: Previous general result for the H-->qq is applied to the H-->tt decay mode where the calculated corrections are significant.

Virtual Supersymmetric Corrections in e^+e^- Annihilation

Depending on their masses, Supersymmetric particles can affect various measurements in Z decay. Among these are the total width (or consequent extracted value of $\alpha_s$), enhancement or suppression of various flavors, and left-right and forward-backward asymmetries. The latter depend on squark mass splittings and are, therefore, a possible test of the Supergravity related predictions. We calculate leading order corrections for these quantities considering in particular the case of light photino and gluino where the SUSY effects are enhanced. In this limit the effect on $\alpha_s$ is appreciable, the effect on $R_b$ is small, and the effect on the asymmetries is extremely small.Comment: 11 pages, LaTeX, 3 figures, revised, a reference adde

On the QCD perturbative expansion for e^+ e^- --> hadrons

We study the perturbative QCD series for the hadronic width of the Z boson. We sum a class of large ``pi^2 terms'' and reorganize the series so as to minimize ``renormalon'' effects. We also consider the renormalization scheme-scale ambiguity of the perturbative results. We find that, with three nontrivial known terms in the perturbative expansion, the treatment of the pi^2 terms is quite important, while renormalon effects are less important. The measured hadronic width of the Z is often used to determine the value of alpha_s(M_Z^2). A standard method is to use the perturbative expansion for the width truncated at order alpha_s^3 in the MS-bar scheme with scale mu = M_Z. We estimate that the determined value of alpha_s(M_Z^2) should be increased by 0.6% compared to the value extracted with this standard method. After this adjustment for pi^2 and renormalon effects, we estimate that the uncertainty in alpha_s(M_Z^2) arising from QCD theory is about 0.4%. This is, of course, much less than the experimental uncertainty of about 5%.Comment: 23 pages, REVTEX3.0, uses epsf.tex to insert figures; with 6 figures in encapsulated postscript for

Quark Mass Corrections to the Z Boson Decay Rates

The results of perturbative QCD evaluation of the ~m_f^2/M_Z^2 contributions to the decay rates in Z--->bb and Z--->hadrons for the quark masses m_f << M_Z are presented. The recent results due to the combination of renormalization group constraints and the results of several other calculations are independently confirmed by the direct computation. Some existing confusion in the literature is clarified. In addition, the calculated O(alpha_s^2) correction to the correlation function in the axial channel is a necessary ingredient for the yet uncalculated axial part of the O(alpha_s^3) mass correction to the Z decay rates. The results can be applied to the \tau hadronic width.Comment: 10 pages, LATeX, +1 figure available upon request, preprint OITS-554 (University of Oregon, USA, September 1994

Top Quark Contribution to Hadronic Decays of the Z-Boson at Alpha_s^2 in QCD

We evaluate the effect of a virtual top quark on the coefficient of $\alpha_{s}^{2}$ in the decay rates $\Gamma(Z \rightarrow {\rm hadrons})$ and $\Gamma(Z \rightarrow b\overline{b} )$. We treat the dependence on the top quark mass exactly instead of using a large mass expansion. The present work completes the evaluation of the $\alpha_{s}^{2}$ contributions to these quantities. The calculation uses both the $\overline{\rm MS}$ and Collins-Wilczek-Zee renormalization prescriptions. The results can be applied to the hadronic decays of the $\tau$-lepton.Comment: 10 pages, REVTeX 3.0 with 4 postscript figures compressed with uufiles, University of Oregon preprint OITS 54

Perturbative QCD Calculations of Total Cross Sections and Decay Widths in Hard Inclusive Processes

A summary of the current understanding of methods of analytical higher order perturbative computations of total cross sections and decay widths in Quantum Chromodynamics is presented. As examples, the total cross section in electron positron annihilation, the hadronic decay rates of the tau lepton and Higgs boson up to O(\alpha_s^2) and O(\alpha_s^3) are considered. The evaluation of the four-loop QED \beta - function at an intermediate step of the calculation is briefly described. The problem of renormalization group ambiguity of perturbative results is considered and some of the existing prescriptions are discussed. The problem of estimation of theoretical uncertainty in perturbative calculations is briefly discussed.Comment: 83 pages, LaTeX, Reviews of Modern Physics style, 14 figures plus figural equations (not included). Hard copy available upon request at [email protected]. To be published in Reviews of Modern Physic